Amid questions about whether the Labour Party will be able to achieve its target of building 1.5 million new homes by 2029, ministers have allocated £1 billion to West Yorkshire and £700 million to South Yorkshire under the previously announced Social and Affordable Housing Programme (SAHP).
Shadow Housing Secretary Sir James Cleverly said the Labour Party has not revealed when the funds will be available for home construction.
The Ministry of Housing, Communities and Local Government said the funding is intended to reduce the number of families stuck on waiting lists, and is expected to create 180,000 social rental homes in England.
This investment is part of the government's previously announced 10-year affordable housing program, totaling £39 billion.
The government said the funding will "accelerate social housing schemes... and meet the need for thousands of new homes for local families."
The government said regional mayors will have the authority to "set the direction of action" by deciding what types of homes will be built where, although bids for the funding will still need to be approved by Homes England.
Reacting to the news, Tracy Brabin, Mayor of West Yorkshire, said: "With council house waiting lists and private rents at breaking point, addressing the housing crisis is the most fundamental step our government could take to build a brighter Britain."
South Yorkshire Mayor, Oliver Coppard, said the money meant everyone in the community could be offered "a high-quality home".
In addition to the social housing fund, mayors have also been allocated a £150 million package for the development of brownfield sites, aimed at creating 1,600 new homes in Yorkshire.
The government said £21 million has been allocated for 841 homes in West Yorkshire, £12.3 million for 492 homes in South Yorkshire, and £73 million for 292 homes in North Yorkshire.
Mayor of York and North Yorkshire, David Scathach, said the funding would enable more affordable homes to be built on brownfield land.
He added: "Our region is home to beautiful rural and coastal towns, but rising rents, costs and second home ownership are pushing up house prices for working families."